My way of finding lengths between 2 pts(complex numbers),what's wrong?

[inv]

[Solved]Length formula to find lengths between 2 pts(complex numbers),what's wrong?

Homework Statement

I've 3 pts U(2i),A(-√3 -i) & B(√3-i),all complex numbers.A question asks me to prove UAB is equilateral.

Homework Equations

|AB|=√{(b-a)^2} for finding lengths.

The Attempt at a Solution

So I try to find two of it's lengths AB and UA.
|AB|=√(b-a)^2
=√{4(3)}
=√12
|UA|=√{a-u}^2
=√(-√3-3i)^2
=√(3-9)
=√-6
The two lengths not same,what's wrong here?

 

[Hootenanny]

In general we can find the modulus of a complex number thus;

$$|z| = \sqrt{z\bar{z}}$$

Also note that $\left(-\sqrt{3}-3i\right)^2 \neq (3-9)$ as you have in your solution for |UA|

 

[inv]

Problem solved and thanks indeed*